The area and perimeter of the trapezium given below is ___

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The area and perimeter of the trapezium given below is ____dm2 and [[2]] dm respectively.

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Detailed Solution

Concept- The area and perimeter of the trapezium is 11.25 dm2 and 14.5 dm.
To solve this question, we need to know the formula of area and perimeter of a trapezium.
seo

The trapezium can be broken into a rectangle and a triangle and the summation of the individual areas of the rectangle and the triangle will be equal to the total area of the trapezium.
For that, we need to know the formulae of the areas of a rectangle and a triangle.
Area of a rectangle = (l×b) where, (l = length of the rectangle) and (b = breadth of the rectangle).
Area of a triangle =

where, (b = Length of base of the triangle) and (h = Altitude of the triangle).
The perimeter of the trapezium = (summation of length of the 4 sides)
Given, dimensions of the trapezium are :
(AB = 5), (BD = 3), (AC = 2.5) and (CD = 4).
Joining DE forms, a rectangle ACDE. Since opposite sides of a rectangle are equal in lengths, then, (AC = DE = 2.5) and (CD = AE = 4)
Therefore, Area of ACDE =

And joining the also forms a triangle, DEB which is a right-angled triangle with right-angle at E (Since, DE and AE are adjacent sides of a rectangle, DE is perpendicular to AE or AB),
Given, (DB = 3) and already calculated, DE = 2.5
Now,
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